When the quaternion measurements are clean, the initial assignment of the desired quaternion in (REF ) ensures the tracking error \(e(t)\)  to converge to the origin under the control law (REF ) and (REF ). The convergence to the origin of the tracking error \(e(t)\)  implies convergence of the quaternion error \(\epsilon (t)\)  in (31) to either of the two disconnected antipodal points on \(S^3\) . Without a careful treatment of the ambiguity, however, it may become sensitive to small quaternion measurement noise [1]}. To deal with this issue, motivated by the recent works [2]}, [3]} this subsection presents a hybrid state-feedback controller. The main idea is to make the switching as in (REF ) each time when a switch condition is satisfied, depending on a potential function \(\mathcal {U}(e)\)  measuring the closeness to one of these two antipodal points.
